Sleep is a given. The brain is learning continuously, not just during sleep. Go back to a section of a piece after 15 minutes doing something else and notice it has become easier.
Sometimes it's even easier after just 1 minute away. I code and play music, and I've made a habit of occasionally walking around the house, petting the dog, then back to where I'm working/practicing. It doesn't take long, but it works strangely well.
Yes. There's something about walking isn't there? Returning attention back to the body and the senses amounts to relaxing after hard concentration. Perhaps petting the dog enhances that, the body being where emotions are felt. Scientists seem to suspect that walking or just standing occasionally is important for health.
To complete the argument about learning: you play the tough section, correcting a few errors. Then you go away for a bit, and during that period the brain updates its hardware to include those corrections. The mistake is to hammer/saw away repeatedly and interfere with what you have already achieved, wasting time and effort. I think the OP kinda acknowledged this by recommending switching at whim between different tasks within a practice session.